The Boston Whaler 17 is a very stable boat and safe boat especially for a small family. You should be able to find one in your price range but it will be older and usually have an older two-stroke motor. Nothing wrong with a two-stroke I run one myself on a 17 Whaler but I mostly use it in the SF Bay and the ocean.
For mountain lakes and shallow rivers a 14-16 foot aluminum boat is a better bet because they handle hitting the occasional rock much better than a fiberglass boat. You can also power a 14 foot aluminum with much less HP which translates to much lower cost. A 9.9 to 15 hp four-stroke motor will work well on a 14 you are not going to win any races but it is very fuel efficient and much less expensive than a 50-90hp motor you need on a 17' Whaler.
All boats are a compromise and there are some things you should think about before purchasing. Like do you want a boat with remote steering (has a steering wheel) or is tiller steering ok (where you sit back by the motor and steer with a handle that is directly attached to the motor). If you decide on remote steering do you want a side console or a center console? Do you want more of a flat bottomed boat like a Jon boat which is better in shallow water and planes easily with low HP but usually beats you up if there are any waves or do you want more of a v-shaped boat which is more comfortable in deeper water and with waves and usually has higher sides like the Lund Alaskan Series but requires somewhat deeper water. Perhaps you want something in between a flat bottom and a v-hull boat like a modified V hull or a flat bottom with a v-shaped bow like the Lund Predator series. Perhaps you want a boat you can put on a roof rack or perhaps you are okay with towing a trailer.
In a boat longer usually means more capacity and a smoother ride. Wider (beam) usually means more stable and less side to side rocking movement. To get an idea of what hull shapes are available you might look at the variety of boat styles that are offered by some manufacturers.
Lund which offers like 26 different boat styles (a few I mentioned above)
https://www.lundboats.com
Bass Pro They have a bunch of different boat styles in various sizes too.
https://www.bassproboatingcenters.co...scrollToResult
Once you decide on hull shape and steering type then start looking in to some of the other manufacturers offering the same style of boat you like there are a bunch of other manufacturers that make great boats. Then ask lots of questions this way you can make a more informed purchase.
Sorry this ran a little long I tried to keep it short...
Regards,
Tim C.
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